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Biometrika 1990 77(2):424-428; doi:10.1093/biomet/77.2.424
© 1990 by Biometrika Trust
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MISCELLANEA

On the construction of a parameter orthogonal to the mean

GORDON E. WILLMOT

Department of Statistics and Actuarial Science, University of Waterloo Waterloo, Ontario N2L 3G1, Canada

It is shown that for many parametric families the condition for a parameter to be orthogonal to the mean takes on a particularly simple form. As a result, it is often possible to obtain analytically an explicit orthogonal parameter, thus providing insight into the many situations involving parametric families in which such a parameter is known to exist. Orthogonal parameterizations are then given for some other models.

Key Words: Compound distribution • Convolution • Maximum likelihood estimation • Power series distribution • Thomas distribution


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